Final answer:
The range of the function after reflection over the x-axis, given the domain points (1,5), (2,1), and (-1,-7), is {(-5), (-1), (7)}.
Step-by-step explanation:
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. The student wants to know the range of a function after it has been reflected over the x-axis. The given domain contains the points (1,5), (2,1), and (-1,-7). To determine the range after reflection, we change the sign of the y-values while keeping the x-values the same because a reflection over the x-axis affects only the y coordinates. This process yields the points (1,-5), (2,-1), and (-1,7). So, the range of the function after reflection is {(-5), (-1), (7)}.